Average Error: 15.5 → 0.9
Time: 5.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right) \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}} \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right) \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (* (cbrt g) (cbrt (sqrt 0.5))) (cbrt (/ (sqrt 0.5) a))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return (cbrt(g) * cbrt(sqrt(0.5))) * cbrt(sqrt(0.5) / a);
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

    \[\sqrt[3]{\frac{g}{2 \cdot a}} \]

  2. Applied div-inv_binary6415.5

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

  3. Applied cbrt-prod_binary640.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}} \]

  4. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{0.5}{a}}} \]

  5. Applied *-un-lft-identity_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{\color{blue}{1 \cdot a}}} \]

  6. Applied add-sqr-sqrt_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}}{1 \cdot a}} \]

  7. Applied times-frac_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt{0.5}}{1} \cdot \frac{\sqrt{0.5}}{a}}} \]

  8. Applied cbrt-prod_binary640.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt{0.5}}{1}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)} \]

  9. Applied associate-*r*_binary640.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{1}}\right) \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}} \]

  10. Simplified0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right)} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}} \]

  11. Final simplification0.9

    \[\leadsto \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right) \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}} \]

Reproduce

herbie shell --seed 2021224 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))